1CGBSV(1) LAPACK driver routine (version 3.2) CGBSV(1)
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6 CGBSV - computes the solution to a complex system of linear equations A
7 * X = B, where A is a band matrix of order N with KL subdiagonals and
8 KU superdiagonals, and X and B are N-by-NRHS matrices
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11 SUBROUTINE CGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
12 INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
14 INTEGER IPIV( * )
16 COMPLEX AB( LDAB, * ), B( LDB, * )
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20 CGBSV computes the solution to a complex system of linear equations A *
21 X = B, where A is a band matrix of order N with KL subdiagonals and KU
22 superdiagonals, and X and B are N-by-NRHS matrices. The LU decomposi‐
23 tion with partial pivoting and row interchanges is used to factor A as
24 A = L * U, where L is a product of permutation and unit lower triangu‐
25 lar matrices with KL subdiagonals, and U is upper triangular with KL+KU
26 superdiagonals. The factored form of A is then used to solve the sys‐
27 tem of equations A * X = B.
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30 N (input) INTEGER
31 The number of linear equations, i.e., the order of the matrix
32 A. N >= 0.
33 KL (input) INTEGER
35 The number of subdiagonals within the band of A. KL >= 0.
36 KU (input) INTEGER
38 The number of superdiagonals within the band of A. KU >= 0.
39 NRHS (input) INTEGER
41 The number of right hand sides, i.e., the number of columns of
42 the matrix B. NRHS >= 0.
43 AB (input/output) COMPLEX array, dimension (LDAB,N)
45 On entry, the matrix A in band storage, in rows KL+1 to
46 2*KL+KU+1; rows 1 to KL of the array need not be set. The j-th
47 column of A is stored in the j-th column of the array AB as
48 follows: AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-
49 KU)<=i<=min(N,j+KL) On exit, details of the factorization: U is
50 stored as an upper triangular band matrix with KL+KU superdiag‐
51 onals in rows 1 to KL+KU+1, and the multipliers used during the
52 factorization are stored in rows KL+KU+2 to 2*KL+KU+1. See
53 below for further details.
54 LDAB (input) INTEGER
56 The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
57 IPIV (output) INTEGER array, dimension (N)
59 The pivot indices that define the permutation matrix P; row i
60 of the matrix was interchanged with row IPIV(i).
61 B (input/output) COMPLEX array, dimension (LDB,NRHS)
63 On entry, the N-by-NRHS right hand side matrix B. On exit, if
64 INFO = 0, the N-by-NRHS solution matrix X.
65 LDB (input) INTEGER
67 The leading dimension of the array B. LDB >= max(1,N).
68 INFO (output) INTEGER
70 = 0: successful exit
71 < 0: if INFO = -i, the i-th argument had an illegal value
72 > 0: if INFO = i, U(i,i) is exactly zero. The factorization
73 has been completed, but the factor U is exactly singular, and
74 the solution has not been computed.
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77 The band storage scheme is illustrated by the following example, when M
78 = N = 6, KL = 2, KU = 1:
79 On entry: On exit:
80 * * * + + + * * * u14 u25 u36
81 * * + + + + * * u13 u24 u35 u46
82 * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
83 a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
84 a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 *
85 a31 a42 a53 a64 * * m31 m42 m53 m64 * * Array
86 elements marked * are not used by the routine; elements marked + need
87 not be set on entry, but are required by the routine to store elements
88 of U because of fill-in resulting from the row interchanges.
89 LAPACK driver routine (version 3.N2o)vember 2008 CGBSV(1)